Answer
$0$
Work Step by Step
\begin{align*}
\lim _{\theta\rightarrow 0} \frac{ 1 -\cos \theta }{\sin\theta } &=\lim _{\theta\rightarrow 0} \frac{ 1 -\cos \theta }{\sin\theta } \frac{\theta}{\theta}\\
&= \lim _{\theta\rightarrow 0} \frac{ 1- \cos \theta }{\theta } \lim _{\theta\rightarrow 0}
\frac{\theta}{\sin \theta}\\
&=0.
\end{align*}
Where we used the facts that $\lim _{\theta\rightarrow 0} \frac{ 1- \cos \theta }{\theta } =0$ and $\lim _{\theta\rightarrow 0} \frac{ \theta }{\sin \theta } =0$
